Evaluation of a Modified Weibull Distribution for Describing the Strength of Ceramic Fibers and Whiskers with Varying Diameters

A modified Weibull distribution is evaluated for characterizing the statistical strength of ceramic fibers and whiskers with varying diameters from filament to filament. Many commercial ceramic fibers and whiskers have a significant range of diameters. A single-modal Weibull distribution is found inadequate to describe the statistical strength of these fibers and whiskers because of the effect of fiber diameter variation on strength. Procedures for extracting distribution parameters for the modified Weibull distribution from experimental data are presented. Comparison of the modified Weibull distribution with the single-modal Weibull distribution is made for the strength data from Nicalon fibers, Nextel (Al₂O₃) fibers, hydridopolysilazalane (HPZ) Si-N-C-O fibers, Al₂O₃ whiskers, Si₃N₄ whiskers, and SiC whiskers. Due to its ability to account for the diameter effect on strength, the modified Weibull distribution can yield a more accurate β value than the single-modal Weibull distribution. The modified Weibull distribution is shown to fit experimental data well and is recommended for characterizing the strength of ceramic fibers and whiskers, the diameters of which vary from filament to filament.